To predict the consequences of human-induced global climate change, we need to understand how climate is linked to biogeography. Energetic constraints are commonly invoked to explain animal distributions, and physiological parameters are known to vary along distributional gradients. But the causal nature of the links between climate and animal biogeography remain largely obscure. Here we develop a bioenergetic model that predicts the feasibility of mammalian hibernation under different climatic conditions. As an example, we use the well-quantified hibernation energetics of the little brown bat (Myotis lucifugus) to parameterize the model. Our model predicts pronounced effects of ambient temperature on total winter energy requirements, and a relatively narrow combination of hibernaculum temperatures and winter lengths permitting successful hibernation. Microhabitat and northern distribution limits of M. lucifugus are consistent with model predictions, suggesting that the thermal dependence of hibernation energetics constrains the biogeography of this species. Integrating projections of climate change into our model predicts a pronounced northward range expansion of hibernating bats within the next 80 years. Bioenergetics can provide the simple link between climate and biogeography needed to predict the consequences of climate change.